Written for advanced undergraduate- and graduate-level students, this book presents the state of the art in sparse and multiscale image and signal processing. It covers linear multiscale transforms, such as wavelet, ridgelet, and curvelet transforms, and non-linear multiscale transforms based on the median and mathematical morphology operators. The book weds theory and practice in examining applications in areas such as astronomy, biology, physics, digital media, and forensics. Topics covered include the wavelet transform, sparsity and noise removal, morphological diversity, and compressed sensing.